We study the Minkowski length L (P) of a lattice polytope P, which is defined to be the largest
number of non-trivial primitive segments whose Minkowski sum lies in P. The Minkowski …

Abstract A lattice (d, k)-polytope is the convex hull of a set of points in dimension d whose
coordinates are integers between 0 and k. Let δ (d, k) be the largest diameter over all lattice …

In this paper we prove new lower bounds for the minimum distance of a toric surface code
C_P defined by a convex lattice polygon P⊂R^2. The bounds involve a geometric invariant …

For a given lattice polytope P⊂R^3, consider the space L_P of trivariate polynomials over a
finite field F_q, whose Newton polytopes are contained in P. We give an upper bound for the …

The Minkowski length of a lattice polytope P is a natural generalization of the lattice diameter
of P. It can be defined as the largest number of lattice segments whose Minkowski sum is …

Lattice polytopes arise naturally in algebraic geometry, analysis, combinatorics, computer
science, number theory, optimization, probability and representation theory. They possess a …

In this paper we show that the diameter of ad-dimensional lattice polytope in 0, k^ n 0, kn is
at most ⌊\left (k-1 2\right) d ⌋⌊ k-1 2 d⌋. This result implies that the diameter of ad …

We describe two different approaches to making systematic classifications of plane lattice
polygons, and recover the toric codes they generate, over small fields, where these match or …

This paper is concerned with the minimum distance computation for higher dimensional toric
codes defined by lattice polytopes in R^n. We show that the minimum distance is …

A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with
exactly i> 0 interior lattice points. We will show that the same bound is true for the …